Question: When Julia is writing a first draft, there is $0.7$ probability that there will be no spelling mistakes on a page. One day, Julia writes a first draft that is $4$ pages long. Assuming that Julia is equally likely to have a spelling mistake on each of the $4$ pages, what is the probability that she will have no spelling mistakes on at least one of them? Round your answer to the nearest hundredth. $P(\text{at least one without mistakes})=$
Answer: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (she writes at least one without spelling mistakes) by calculating the probability of its complement (she makes mistakes on every page), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one without mistakes})=1-P(\text{mistakes on all }4)$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one without mistakes}) \\\\ &=1-P(\text{mistakes on all }4) \\ \\ &=1-(0.3)^{4} \\ \\ &= 1-0.0081 \\ \\ &= 0.9919\end{aligned}$ Answer $P(\text{at least one without mistakes}) \approx 0.99$